## Portfolio Performance Evaluation

Unit 4 SAPM Notes

Jensen's Portfolio Performance Measure

**Jenson Model**

Jensen's model proposes another risk adjusted performance measure.
This measure was developed by Michael Jensen and is sometimes referred to as
the Differential Return Method. This measure involves evaluation of the returns
that the fund has generated vs. the returns actually expected out of the fund
given the level of its systematic risk. The surplus between the two returns is
called Alpha, which measures the performance of a fund compared with the actual
returns over the period. Required return of a fund at a given level of risk (**b**)
can be calculated as:

**R _{t} – R = a + b (R_{m} – R)**

Where, R_{t} = Portfolio Return

R = Risk less return

a = Intercept the graph that measures
the forecasting ability of the portfolio manager.

b = Beta coefficient, a measure of
systematic risk

R_{m} = Return of the market
portfolio

Thus, Jensen’s equation involves two steps:

(i) First he calculates what the return of a given portfolio
should be on the basis of b, R_{m }and R.

(ii) He compares the actual realised return of the portfolio with
the calculated or predicted return. Greater the excess of realised return over
the calculated return, better is the performance of the portfolio.

Limitation of this model is that it considers only systematic risk not the entire risk associated with the fund and an ordinary investor can not mitigate unsystematic risk, as his knowledge of market is primitive.

Graphic representation of Jensen’s model is a given in the following figure:

The figure shows three lines showing negative, neutral and
positive values. The negative line shows that the management of the performed
portfolio is inferior. The positive line shows that superior quality of
management of funds. The neutral value shows that the performance of the fund
is similar to the performance of the market portfolio.

A comparison between the three models shows that the intercept of
the line is Sharpe and Treynor models is always at the origin, where as
Jensen’s model it may be at the origin (a = 0), above the origin (a > 0) and
even be below the origin indicating a negative value (a < 0). The risk
adjusted measures have been criticized for using a market surrogate instead of the
true market portfolio. These measures have been unable to statistically
distinguish luck or change from skill except over very long period of time.
Moreover, these models rely heavily on the validity of CAPM. If in estimating
the measures the analyst assumes the wrong from of the CAPM in the market
place, he will get based measure of performance, usually in favour of low risk
portfolios.

**Advantages of ****Jensen's Portfolio Performance Measure**

a) This model is very easy to interpret.

b) It helps to measure how much of the
portfolio's rate of return is attributable to deliver above-average returns,
adjusted for market risk. The higher the ratio, the better the risk adjusted
returns.

c) Because it is estimated from a regression equation, it is
possible to make statements about the statistical significance of the manager’s
skill level.

d) It is flexible enough to allow for alternative
models of risk and expected return than the CAPM.

**Disadvantages
of ****Jensen's Portfolio Performance Measure**

a) Weakness of Treynor’s ratio is that it requires an estimate of
beta, which can differ a lot depending on the source which in turn can lead to
mis-measurement of risk adjusted return. Many investors accomplish that a beta
cannot give a clear picture of risk involved with the investment.

b) It does not consider the advantage of a diversified portfolio.

c) Jensen’s alpha doesn’t take the portfolio’s volatility and
takes into account, only the expected return.

d) It will miss out on characteristics such as returns kurtosis
and skewness, which are of great importance in determining whether you’ll go
broke before you realize profits.